scholarly journals Boundedness for multilinear Marcinkiewicz operators on Triebel-Lizorkin spaces

2005 ◽  
Vol 33 (0) ◽  
pp. 73-84
Author(s):  
Lanzhe Liu
Keyword(s):  
Marcinkiewicz Operators

scholarly journals Weighted boundedness of multilinear integral operators for the endpoint cases

2022 ◽  
Vol 7 (4) ◽  
pp. 5690-5711
Author(s):  
Ancheng Chang ◽  
Keyword(s):  
Integral Operators ◽  
Multilinear Operators ◽  
Riesz Operator ◽  
Marcinkiewicz Operators

<abstract><p>We prove the weighted boundedness for the multilinear operators associated to some integral operators for the endpoint cases. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.</p></abstract>

scholarly journals Sharp maximal function estimates and boundedness for commutators associated with general integral operator

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 137-151 ◽  
Author(s):  
Lanzhe Liu
Keyword(s):  
Integral Operator ◽  
Maximal Function ◽  
Lipschitz Functions ◽  
Sharp Maximal Function ◽  
Lizorkin Space ◽  
Riesz Operator ◽  
General Integral ◽  
General Integral Operator ◽  
Marcinkiewicz Operators

In this paper, we establish the sharp maximal function estimates for the commutator associated with some integral operator with general kernel and the weighted Lipschitz functions. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey and Triebel-Lizorkin space. The operator includes Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.

Continuity of Multilinear Marcinkiewicz Operators for the Extreme Cases of 𝑝

2005 ◽  
Vol 12 (4) ◽  
pp. 683-691
Author(s):  
Lanzhe Liu
Keyword(s):  
Continuity Properties ◽  
Marcinkiewicz Operators

Abstract We prove the continuity properties of multilinear Marcinkiewicz operators for the extreme cases of 𝑝.

scholarly journals Boundedness for multilinear Marcinkiewicz operators on certain Hardy spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 87-96
Author(s):  
Liu Lanzhe
Keyword(s):  
Hardy Spaces ◽  
Marcinkiewicz Operators

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.

BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES

2015 ◽  
Vol 99 (3) ◽  
pp. 380-398 ◽  
Author(s):  
FENG LIU ◽  
SUZHEN MAO
Keyword(s):  
Radial Function ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Operators ◽  
L Log L

In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function $h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley $g_{{\it\lambda}}^{\ast }$-functions are given.

Continuity for Multilinear Marcinkiewicz Operators on Certain Hardy Spaces

2003 ◽  
Vol 10 (4) ◽  
pp. 717-728
Author(s):  
Lanzhe Liu
Keyword(s):  
Hardy Spaces ◽  
Marcinkiewicz Operators

Abstract In this paper, the continuity of multilinear Marcinkiewicz operators on certain Hardy and Herz–Hardy spaces is obtained.

Sign in / Sign up

Export Citation Format

Share Document